If I roll a regular six-sided die, what is the probability that the score is divisible by three?
So the first thing we’re gonna do is actually write out all the possible scores I could get from a six-sided die. So I’ve got one, two, three, four, five, and six. So now the next stage is actually to see which ones of these scores are actually divisible by the number three.
Well, one isn’t divisible by three. Two isn’t divisible by three. Three is divisible by three, because if you do three divided by three, we just get one. Four isn’t divisible by three. Five isn’t divisible by three. But finally, six is divisible by three. And that’s because if we have six divided by three, we get two.
Okay, great! We’ve now determined which of our scores are divisible by three. Now in order to actually work out the probability that the score is divisible by three, we can actually remember this little rule that the probability of an event happening is actually the number of times that event occurs divided by the total outcomes or the total number of outcomes.
So therefore, we can say that the probability that the score is gonna be divisible by three is equal to our number of events — so what that means is number of times that actually the score is divisible by three; so that is number three, so that’s one, and number six, that’s two — then divided by the total number of outcomes.
Well, we know there are six possible outcomes if we could roll a dice cause we get the numbers one to six. Ok, great! So we’ve found the answer that we needed cause we found the probability that the score is divisible by three cause it’s equal to two over six.
But what I always like to do here is cancel, if possible. So we’re gonna simplify. So then if we actually divide the numerator and denominator by two, because two is a common factor, we can say that if I roll a regular six-sided die, the probability that the score is divisible by three is gonna be equal to one-third.